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针对采用直接法求解轨迹优化问题中精度和效率之间的矛盾,提出了基于二代小波轨迹优化节点自适应加密.采用RK(Runge-Kutta)离散方法将原轨迹优化问题转化为非线性规划问题,并采用成熟的非线性规划算法求解.对控制或状态函数进行小波变换得到小波系数,基于小波系数和二分节点的对应关系,根据小波系数的幅值确定下一个迭代步所使用的节点并进行序列优化.算例结果表明:通过设置合适的小波系数阀值,采用较少的时间离散节点即可使优化结果达到预定的精度.与高斯伪谱法软件相比,节点个数大约减少10%,最优指标的精度大约提高1个数量级.
Aiming at the contradiction between the accuracy and the efficiency in solving the trajectory optimization problem by the direct method, this paper proposes an adaptive node encryption algorithm based on the second-generation wavelet trajectory. The RK (Runge-Kutta) method is used to transform the original trajectory optimization problem into a nonlinear programming problem , And is solved by the mathematic nonlinear programming algorithm.Wavelet transform is performed on the control or state function to get the wavelet coefficients. Based on the correspondence between the wavelet coefficients and the bisection nodes, the nodes used in the next iteration step are determined according to the amplitude of the wavelet coefficients Sequence optimization.Experimental results show that the optimal results can reach the predetermined accuracy by setting the appropriate wavelet coefficient threshold and using less time discrete nodes.Compared with the Gaussian pseudospectrum software, the number of nodes is reduced by about 10% , The accuracy of the optimal index increased by about 1 order of magnitude.